Finite Group Databasebeta

← Group #10692555

Character table — Group #10692555

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222444444444444444444444888888888812121212121212121212121212121212161616161616161616161616242424244848
order12222234444446664444444444466121212121212121212121212121212121212888888888888888888882424242424242424444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1
χ61111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ71111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111
χ81111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111111-1-1
χ91111111-1-1-1-1-1-1111-11111-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−ii−ii−iii−i−iii−i−i11-1-11-1
χ101111111-1-1-1-1-1-1111-11111-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−ii−ii−i−iii−i−iii-1-111-11
χ111111111-1-1-1-1-1-1111-11111-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiii−ii−iii−i−iii−i−i-1-111-11
χ121111111-1-1-1-1-1-1111-11111-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−ii−ii−i−iii−i−iii11-1-11-1
χ131111111-1-1-1-1-1-1111-111-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiii−i−iiii−i−i−i−iii11-1-1-11
χ141111111-1-1-1-1-1-1111-111-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−iii−i−i−iiiii−i−i-1-1111-1
χ151111111-1-1-1-1-1-1111-111-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−ii−i−iiii−i−i−i−iii-1-1111-1
χ161111111-1-1-1-1-1-1111-111-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−iii−i−i−iiiii−i−i11-1-1-11
χ1722222222222-2-2222-2-2-22222-2-2-2-222-2-2-2-22222-2-222-2-222-2-20000000000000000000000000000000000
χ1822222222222-2-2222-2-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-222-2-2220000000000000000000000000000000000
χ192222222-2-2-2-2222222-2-222-2-2-2-222222222-2-2-2-2-2-222-2-2-2-2220000000000000000000000000000000000
χ202222222-2-2-2-2222222-2-2-2-22222-2-2222222-2-2-2-2-2-2-2-22222-2-20000000000000000000000000000000000
χ21222222-1222222-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-1000000
χ22222222-1222222-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-211111111000000
χ23222222-1222222-1-1-1222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111000000000000000022-2-2-1-1-1-11111000000
χ24222222-1222222-1-1-1222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-2221111-1-1-1-1000000
χ25222222-12222-2-2-1-1-1-2-2-22222-2-2-2-2-1-11111-1-1-1-111-1-111-1-11100000000000000000000−i3i3−i3i3−i3i3−i3i3000000
χ26222222-12222-2-2-1-1-1-2-2-22222-2-2-2-2-1-11111-1-1-1-111-1-111-1-11100000000000000000000i3−i3i3−i3i3−i3i3−i3000000
χ27222222-12222-2-2-1-1-1-2-2-2-2-2-2-22222-1-11111-1-1-1-11111-1-111-1-100000000000000000000−i3i3−i3i3i3−i3i3−i3000000
χ28222222-12222-2-2-1-1-1-2-2-2-2-2-2-22222-1-11111-1-1-1-11111-1-111-1-100000000000000000000i3−i3i3−i3−i3i3−i3i3000000
χ29222222-1-2-2-2-222-1-1-12-2-222-2-2-2-222-1-1-1-1-1-1111111-1-11111-1-1000000000000000000003−3−333−3−33000000
χ30222222-1-2-2-2-222-1-1-12-2-222-2-2-2-222-1-1-1-1-1-1111111-1-11111-1-100000000000000000000−333−3−333−3000000
χ31222222-1-2-2-2-222-1-1-12-2-2-2-22222-2-2-1-1-1-1-1-111111111-1-1-1-111000000000000000000003−3−33−333−3000000
χ32222222-1-2-2-2-222-1-1-12-2-2-2-22222-2-2-1-1-1-1-1-111111111-1-1-1-11100000000000000000000−333−33−3−33000000
χ33222222-1-2-2-2-2-2-2-1-1-1-22222-2-222-2-2-1-111111111-1-1-1-1-1-1111100000000000000002i−2i2i−2i−i−iii−i−iii000000
χ34222222-1-2-2-2-2-2-2-1-1-1-22222-2-222-2-2-1-111111111-1-1-1-1-1-111110000000000000000−2i2i−2i2iii−i−iii−i−i000000
χ35222222-1-2-2-2-2-2-2-1-1-1-222-2-222-2-222-1-111111111-1-11111-1-1-1-100000000000000002i−2i−2i2i−i−iiiii−i−i000000
χ36222222-1-2-2-2-2-2-2-1-1-1-222-2-222-2-222-1-111111111-1-11111-1-1-1-10000000000000000−2i2i2i−2iii−i−i−i−iii000000
χ372222-2-222-22-222222-22-200000000-2-222-2-22-22-22-2000000000000000022-2-222-2-2000000000000000000
χ382222-2-222-22-222222-22-200000000-2-222-2-22-22-22-20000000000000000-2-222-2-222000000000000000000
χ392222-2-222-22-2-2-22222-2200000000-2-2-2-2222-22-2-22000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000
χ402222-2-222-22-2-2-22222-2200000000-2-2-2-2222-22-2-2200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000
χ412222-2-22-22-2222222-2-2200000000-2-222-2-2-22-22-220000000022-2-2-2-22200000000000000000000000000
χ422222-2-22-22-2222222-2-2200000000-2-222-2-2-22-22-2200000000-2-22222-2-200000000000000000000000000
χ432222-2-22-22-22-2-222222-200000000-2-2-2-222-22-222-200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ442222-2-22-22-22-2-222222-200000000-2-2-2-222-22-222-20000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ452-2-222-222-2-2200-22-20002i−2i2i−2i00002-200002-2-22002i−2i002i−2i002−22−22−22−2−i2i2−i2i2−i2i2−i2i2000000000000000000
χ462-2-222-222-2-2200-22-20002i−2i2i−2i00002-200002-2-22002i−2i002i−2i00−22−22−22−22i2−i2i2−i2i2−i2i2−i2000000000000000000
χ472-2-222-222-2-2200-22-2000−2i2i−2i2i00002-200002-2-2200−2i2i00−2i2i002−22−22−22−2i2−i2i2−i2i2−i2i2−i2000000000000000000
χ482-2-222-222-2-2200-22-2000−2i2i−2i2i00002-200002-2-2200−2i2i00−2i2i00−22−22−22−22−i2i2−i2i2−i2i2−i2i2000000000000000000
χ492-2-222-22-222-200-22-20002i−2i−2i2i00002-20000-222-2002i−2i00−2i2i00−i2i2−i2i2i2−i2i2−i2−22−222−22−2000000000000000000
χ502-2-222-22-222-200-22-20002i−2i−2i2i00002-20000-222-2002i−2i00−2i2i00i2−i2i2−i2−i2i2−i2i22−22−2−22−22000000000000000000
χ512-2-222-22-222-200-22-2000−2i2i2i−2i00002-20000-222-200−2i2i002i−2i00−i2i2−i2i2i2−i2i2−i22−22−2−22−22000000000000000000
χ522-2-222-22-222-200-22-2000−2i2i2i−2i00002-20000-222-200−2i2i002i−2i00i2−i2i2−i2−i2i2−i2i2−22−222−22−2000000000000000000
χ532-2-22-22222-2-200-22-200000002-22-2-22000022-2-200002-2002-2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000000000
χ542-2-22-22222-2-200-22-200000002-22-2-22000022-2-200002-2002-2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000000000
χ552-2-22-22222-2-200-22-20000000-22-22-22000022-2-20000-2200-22−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2000000000000000000
χ562-2-22-22222-2-200-22-20000000-22-22-22000022-2-20000-2200-22i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2000000000000000000
χ572-2-22-222-2-22200-22-200000002-2-22-220000-2-22200002-200-222−2−22−222−22−2−22−222−2000000000000000000
χ582-2-22-222-2-22200-22-200000002-2-22-220000-2-22200002-200-22−222−22−2−22−222−22−2−22000000000000000000
χ592-2-22-222-2-22200-22-20000000-222-2-220000-2-2220000-22002-22−2−22−222−2−222−22−2−22000000000000000000
χ602-2-22-222-2-22200-22-20000000-222-2-220000-2-2220000-22002-2−222−22−2−222−2−22−222−2000000000000000000
χ614444-4-4-24-44-444-2-2-2-44-40000000022-2-222-22-22-22000000000000000000000000000000000000000000
χ624444-4-4-24-44-4-4-4-2-2-24-44000000002222-2-2-22-222-2000000000000000000000000000000000000000000
χ634444-4-4-2-44-4444-2-2-2-4-440000000022-2-2222-22-22-2000000000000000000000000000000000000000000
χ644444-4-4-2-44-44-4-4-2-2-244-4000000002222-2-22-22-2-22000000000000000000000000000000000000000000
χ6544-4-400400004-44-4-400000000000004-4000000000000000000000000000000000000000000002-22-200
χ6644-4-400400004-44-4-400000000000004-400000000000000000000000000000000000000000000-22-2200
χ6744-4-40040000-444-4-40000000000000-44000000000000000000000000000000000000000000002-2-2200
χ6844-4-40040000-444-4-40000000000000-4400000000000000000000000000000000000000000000-222-200
χ694-4-444-4-24-4-44002-220004i−4i4i−4i0000-220000-222-200−2i2i00−2i2i000000000000000000000000000000000000
χ704-4-444-4-24-4-44002-22000−4i4i−4i4i0000-220000-222-2002i−2i002i−2i000000000000000000000000000000000000
χ714-4-444-4-2-444-4002-220004i−4i−4i4i0000-2200002-2-2200−2i2i002i−2i000000000000000000000000000000000000
χ724-4-444-4-2-444-4002-22000−4i4i4i−4i0000-2200002-2-22002i−2i00−2i2i000000000000000000000000000000000000
χ734-4-44-44-244-4-4002-2200000004-44-42-20000-2-2220000-2200-220000000000000000000000000000000000
χ744-4-44-44-244-4-4002-220000000-44-442-20000-2-22200002-2002-20000000000000000000000000000000000
χ754-4-44-44-2-4-444002-2200000004-4-442-2000022-2-20000-22002-20000000000000000000000000000000000
χ764-4-44-44-2-4-444002-220000000-444-42-2000022-2-200002-200-220000000000000000000000000000000000
χ7788-8-800-400008-8-4440000000000000-4400000000000000000000000000000000000000000000000000
χ7888-8-800-40000-88-44400000000000004-400000000000000000000000000000000000000000000000000
χ798-88-8008000000-8-8800000000000000000000000000000000000000000000000000000000000000000
χ808-88-800-400000044-400000000000000043−43000000000000000000000000000000000000000000000000
χ818-88-800-400000044-4000000000000000−4343000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).